[It slightly bothers me that the last few posts are mostly MineCraft-related. But as Leo has been getting more and more interested in nuances of MineCraft, I’m trying to guide this interest toward math instead of evil. (And “evil” is MineCraft is quite a lot less evil than with many other things he could be getting addicted to.) (Some day I’ll talk about MineCraft addiction management strategies … when I figure some out!)]

Interestingly, in MineCraft, the term “seed” makes for a convenient pun; Leo understood perfectly that the “seed” is what the world is grown from. But in reality, of course, is comes from the concept of a random number seed, which is how the pseudo-random number generator uses to create the random stream that starts off the whole world, and everything in it. This, of course, is how it’s possible to publish the seed, as in the web page above, and others can get back to the same exact (initial) world.

So I turned this into a lesson plan on random numbers, pseudo-random numbers, determinism and non-determinism, and one of Leo’s favorite topics: Quantum Computing and cryptography.

Leo got right away that 4+5 is determistic, and if you were to print the result in a loop (bottom right scribble) you’d get 9 every time, but 4+Rand(10) would randomly give you a number between 5 and 14. (I’m using 1-origin — someday I’ll go into that with Leo … actually, I may have already at some point.) Note, also at the bottom left the important observation that “All non-quantum computers are DETERMINISTIC.”

So, the mystery is:

To translate my scribbles:

All (non-quantum) computers are deterministic.

Rand(#) [which is a computer function] seems to be non-deterministic. (We tried this on the iPad in the BASIC interpreter.)

The mystery (apparent paradox!) is: How does Rand work? (We had a brief passing philosophical discussion about paradox v. conundrum.)

The answer, of course, is:

PSEUDO-RANDOMIZATION – Ensued a long interesting discussion of possible pseudo-randomization algorithms, the meaning of “Mod” (the modulo wheel at the bottom center), and so forth. (This board had lots of erasures; You’re only seeing the end product!)

The key concept, which closes the loop on MineCraft seeds, is that the computer needs to have something external in order to seed the pseudo-randomization. That’s what the box around MineCraft is. We talked a lot about where the computer could get a seed. One place is obviously that you give it a specific seed. In that case what’s external is you! But what about when you don’t give it a seed? (Leo’s initial solution, of course, was to use Rand() … 🙂 After explaining why this wasn’t going to work (can you say: “infinite regress”?) And quantum fluctuations, I posed the following problem: Suppose that you were locked in the kitchen with all the lights off at night (we actually did this exercise, of course), and needed a pseudo-random seed…. It only took a few seconds to get the right answer to this one:

As I’ve mentioned in other posts, Leo and I occasionally read philosophy, and discuss philosophical questions. (Example: What happens to you when we clone your body, but without a brain, and then move your brain into the new, cloned body? Most adults think you’re where your brain is; Leo disagrees!) Our favorite books on this are these two:

Anyway, so we were playing Monopoly. (Which Leo pronounces like two words: “Mono Poly”, which, if you think about it, gives a whole new concept to what a monopoly is!)

He was reading the FAQ:

To which Leo asked: “What happens if we make a new rule that says we can’t make new rules?” …”It’s a Paradox!” … and he burst into laughter!

Recently I’ve been explicitly discussing philosophical questions with Leo. For example, this morning in the car we talked about mind body problems (If your brain was put into a clone of your body, which one is you? If parts of you were slowly replaced with a computer, all the way up to your brain being replaced by an AI, are you still there?), animal ethics (If cows and chickens could talk like people, would we still eat them?), friendship (Does it make sense to have two best friends? — Actually, in retrospect this might be more like a semantics/logic problem than a problem about friendship…more on this below), and basic ethics (If you look at someone else’s test that’s cheating, but suppose that you look at their test and see that they were wrong about something, and you tell them. Are you cheating? Is your friend cheating? Or at you both cheating? What if he does v. doesn’t change his answer.)

Leo actually had some really interesting answer to these. For example, he insisted that even though his brain was in the clone body, that his body was still him. Also, I asked him a question adapted from an ethical issues page at The Center for Philosophy for Children about what he should do if the teacher asks the class to draw a picture of their best friend. I asked whether there was anything wrong with that request, and he pointed out that people can have multiple best friends, which I hadn’t expected at all. (And which led to the discussion of whether you could have two best friends, mentioned above.) When I explained the problem that is mentioned in The Center’s discussion (linked above), that some popular kids would get a lot of drawings, while un-popular kids would get none, he had the idea that people should draw un-popular kids instead of their best friend, which although not what I would have thought of, is creative.

We talked about how, unlike math problems (according to me), some philosophical problems didn’t seem to have a correct answer. Leo immediately pointed out that some math problems don’t either, like the Godel paradox and zero divided by zero. Uh oh….! 🙂

There are some, although not many, online resources for philosophical discussions with children:

In a previous post I mentioned a great little set of YouTube videos called “8-bit Philosophy”, which address serious philosophical issues in a fun, and weirdly retro way. (I don’t know if the folks who make these are aware of the pun of making videos about dead philosophers that parody dead 1970s video games…but regardless of their awareness, the effect is great because it really grabs kids’ attention.)

In another post I sang the praises of BrainPop, which costs a tiny amount of money, and is well worth the price! But there’s also lots of great free educational material out on YouTube. I’m not talking about the horrible, boring, education-and-mind destroying videos from any of the many MOOC panderers, nor from the academy whose name I won’t even mention in order so as not to give them link strength, but whose initials are KA.

Rather, there are some extremely well made, intelligent — sometimes brilliant — often hysterically funny, and always engaging educational videos available for free on YouTube. I obviously don’t have time to describe them all, nor even to watch them all!. Below I just give a bunch of links to some great examples, and you can generalize for yourself.

The one standout that deserves a little explanation is, TED Ed. Now, the main TED talks are, IMHO, a pile of self-aggrandizing, blow-hard, badly-made, marketing crap. (To be fair, there are some good TED talks, but they’re few and far between. The only one that comes to mind is this one: Arthur Benjamin: Lightning calculation and other “Mathemagic”) But please don’t confuse TED with TED Ed; TED Ed is completely different. Here are some great examples of TED Ed:

So Even if you hate TED talks as much as I do, I encourage you to give TED Ed a look.

Okay, enough about TED Ed. I’m sorry that I don’t have the energy to sing the praises quite as highly for these others as I have for TED Ed, but you should check these out, because they’re often as good, and sometimes better than some of the TED Eds. (The TED Eds are just consistently of amazing quality, whereas these others are good, sometimes great, but not as consistently great as TED Ed.)

I’m just going to give a bunch somewhat intentionally unorganized links below; I encourage you to explore more of each similar vids, and please if you have others, don’t hesitate to comment and add them.

So, without further blather, here below please find a smattering of youtube that I think is great (but you’ll make up your own mind, of course):